Paper 2008/530
Fast hashing to G2 on pairing friendly curves
Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J. Dominguez Perez and Ezekiel J. Kachisa
Abstract
When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of the two elliptic curve groups of prime order $r$ involved in the pairing. Of these $G_1$ is a group of points on the base field $E(\F_p)$ and $G_2$ is instantiated as a group of points with coordinates on some extension field, over a twisted curve $E'(\F_{p^d})$, where $d$ divides the embedding degree $k$. While hashing to $G_1$ is relatively easy, hashing to $G_2$ has been less considered, and is regarded as likely to be more expensive as it appears to require a multiplication by a large cofactor. In this paper we introduce a fast method for this cofactor multiplication on $G_2$ which exploits an efficiently computable homomorphism.
Metadata
- Available format(s)
- Category
- Implementation
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Tate PairingAddition Chains
- Contact author(s)
- mike @ computing dcu ie
- History
- 2008-12-19: received
- Short URL
- https://ia.cr/2008/530
- License
-
CC BY